Salmonella typhi: Dose Response Experiments

General Overview

Salmonella enterica, serovar Typhi (S. Typhi for short, but formerly known as Salmonella typhi or Salmonella typhosa) causes typhoid fever. Paratyphoid fever is a similar syndrome (but less common and less severe than typhoid fever) caused by Salmonella enterica, serovar Typhi (S. Paratyphi). Typhoid and paratyphoid fevers are also jointly known as enteric fever. Other Salmonella enterica serovars (e.g., Enteritidis, Typhimurium) cause a gastroenteritis known as salmonellosis.

S. Typhi and S. Paratyphi only infect humans and are transmitted by the fecal-oral route. Disease may include any combination of the following: cough, constipation, diarrhea, abdominal pain, anorexia, rose spots on the torso, or fever. S. Typhi may also be shed asymptomatically for years in the feces of chronic carriers.

http://www.cdc.gov/nczved/divisions/dfbmd/diseases/typhoid_fever/

Summary of data

There have been two feeding studies in male prisoners of the Quailes strain of S. Typhi (which was named Salmonella typhosa at that time).

Other model fits to these data have been published. However, these model fits exclude some of the experimental data for unclear reasons.

Recommended Model

The pooled model of experiment number 79 and 80 is the recommended model. Pooling is statistically accepted and it gives improvement in fits.

Exponential and betapoisson model.jpg

ID	Exposure Route	# of Doses	Agent Strain	Dose Units	Host type	Μodel	LD50/ID50	Optimized parameters	Response type	Reference
79	oral (in milk)	3.00	Quailes	CFU	human	beta-Poisson	3.45E+06"	a = 1.11E-01 N₅₀ = 3.45E+06	disease	Hornick, R. B., Greisman, S. ., Woodward, T. E., DuPont, H. L., Dawkins, A. T., & Snyder, M. J. (1970). Typhoid fever: pathogenesis and immunologic control. The New England Journal of Medicine, 283, 13.
79, 80	oral (in milk)	8.00	Quailes	CFU	human	beta-Poisson	1.11E+06	a = 1.75E-01 N₅₀ = 1.11E+06	disease	Hornick, R. ., Woodward, T. ., McCrumb, F. ., Snyder, M. ., Dawkins, A. ., Bulkeley, J. ., … Corozza, F. . (1966). Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness. Transactions of the Association of American Physicians, 79, 361-367. Retrieved from https://pubmed.ncbi.nlm.nih.gov/5929469/
80	oral (in milk)	5.00	Quailes	CFU	human	beta-Poisson	8.53E+05	a = 2.03E-01 N₅₀ = 8.53E+05	disease	Levine, M. M., DuPont, H. L., Formal, S. B., Hornick, R. B., Takeuchi, A. ., Gangarosa, E. J., … Libonati, J. P. (1973). Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery. Journal of Infectious Diseases, 127, 3.

Exposure Route:

oral (in milk)

# of Doses:

3.00

Agent Strain:

Quailes

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

3.45E+06"

Optimized parameters: a = 1.11E-01 N₅₀ = 3.45E+06

Response type:

disease

Reference:

Typhoid fever: pathogenesis and immunologic control

**Model data for S. Typhi (Quailes) in humans**
Dose	Disease	No disease	Total
1E+05	28	76	104
1E+07	15	15	30
1E+09	4	0	4

**Goodness of fit and model selection**
Model	Deviance	Δ	Degrees of freedom	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	124	121	2	3.84 0	5.99 0
Beta Poisson	2.87	121	1	3.84 0	3.84 0.0905
Beta-Poisson fits better than exponential; cannot reject good fit for beta-Poisson.

**Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations**
Parameter	MLE estimate	Percentiles
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
α	1.11E-01	3.19E-02	4.80E-02	5.49E-02	1.96E-01	2.17E-01	2.59E-01
N₅₀	3.45E+06	4.81E+05	6.95E+05	8.50E+05	9.53E+07	2.24E+08	4.19E+09

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

Highest quality

Exposure Route:

oral (in milk)

# of Doses:

8.00

Agent Strain:

Quailes

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

1.11E+06

Optimized parameters: a = 1.75E-01 N₅₀ = 1.11E+06

Response type:

disease

Reference:

Study of induced typhoid fever in man. I. Evaluation of vaccine effectiveness

**Model data for S. Typhi (Quailes) in humans**
Dose	Disease	No disease	Total
1000	0	14	14
1E+05	28	76	104
1E+05	32	84	116
1E+07	15	15	30
1E+07	16	16	32
1E+08	8	1	9
1E+09	4	0	4
1E+09	40	2	42

**Goodness of fit and model selection**
Model	Deviance	Δ	Degrees of freedom	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	419	406	7	3.84 0	14.1 0
Beta Poisson	13.8	406	6	3.84 0	12.6 0.0321
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

**Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations**
Parameter	MLE estimate	Percentiles
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
α	1.75E-01	1.21E-01	1.32E-01	1.39E-01	2.23E-01	2.34E-01	2.58E-01
N₅₀	1.11E+06	5.13E+05	6.10E+05	6.72E+05	2.00E+06	2.28E+06	2.95E+06

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

Exposure Route:

oral (in milk)

# of Doses:

5.00

Agent Strain:

Quailes

Dose Units:

CFU

Host type:

human

Μodel:

beta-Poisson

LD50/ID50:

8.53E+05

Optimized parameters: a = 2.03E-01 N₅₀ = 8.53E+05

Response type:

disease

Reference:

Pathogenesis of Shigella dysenteriae 1 (Shiga) Dysentery

**Model data for S. Typhi (Quailes) in humans**
Dose	Disease	No disease	Total
1000	0	14	14
1E+05	32	84	116
1E+07	16	16	32
1E+08	8	1	9
1E+09	40	2	42

**Goodness of fit and model selection**
Model	Deviance	Δ	Degrees of freedom	χ²_0.95,1 p-value	χ²_0.95,m-k p-value
Exponential	293	284	4	3.84 0	9.49 0
Beta Poisson	8.63	284	3	3.84 0	7.81 0.0346
Neither the exponential nor beta-Poisson fits well; beta-Poisson is less bad.

**Optimized parameters for the beta-Poisson model, from 10000 bootstrap iterations**
Parameter	MLE estimate	Percentiles
Parameter	MLE estimate	0.5%	2.5%	5%	95%	97.5%	99.5%
α	2.03E-01	1.33E-01	1.49E-01	1.57E-01	2.74E-01	2.89E-01	3.27E-01
N₅₀	8.53E+05	3.38E+05	4.28E+05	4.80E+05	1.62E+06	1.85E+06	2.49E+06

Parameter scatter plot for beta Poisson model ellipses signify the 0.9, 0.95 and 0.99 confidence of the parameters.

beta Poisson model plot, with confidence bounds around optimized model

Salmonella typhi: Dose Response Experiments Dose response experiments

General Overview

Summary of data

Recommended Model

References